Question

Elena says questions A and B are not equivalent.

Equation A: 13 - 5x = 48
Equation B: 5x = 35
Which of the following statements is true?
a) Elena is correct, the equations are not equivalent.
b) Elena is incorrect, the equations are equivalent.
c) Elena is correct for certain values of x.
d) Elena is incorrect for certain values of x.

Answer 1

Elena is correct; the two equations are not equivalent as they yield different values for x and represent different relationships. Equation A ends up being '5x = -35' after manipulation, which is not the same as '5x = 35' from Equation B.

Step-by-step explanation:

Elena is examining whether two equations are equivalent or not. Let's analyze the equations:

Equation A: 13 - 5x = 48
Equation B: 5x = 35

To see if these equations are equivalent, we can manipulate Equation A to solve for 5x. Subtracting 13 from both sides of Equation A, we get:

-5x = 48 - 13

-5x = 35

If we multiply both sides of this equation by -1, we obtain:

5x = -35

So, after simplifying Equation A, we can see that it would state that 5x equals negative 35, which is not the same as positive 35 as in Equation B. Hence, Elena is correct; the two equations are not equivalent. This is because the two equations would yield different values of x, and they do not represent the same relationship.
Therefore, the correct answer to whether or not the equations are equivalent is:

a) Elena is correct, the equations are not equivalent.